The spacing between these stripes squishes together tightly inside the cylinder boundary, physically demonstrating the slowing down of light due to the higher refractive index.

https://youtu.be/LR79WU52X0E

<aside> 👏

1. https://www.instagram.com/reel/DePBfjIh5DM/?utm_source=ig_web_copy_link&stkn=MzRlODBiNWFlZA==
2. https://via-dean.gitbook.io/all/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/inhomogeneous-helmholtz-wave-propagation-and-refractive-scattering-model
3. https://bsky.app/profile/researcherdean.bsky.social/post/3mxel54w3bc2g
4. https://x.com/d54223/status/2108189421908762877?s=20
5. https://hackmd.io/@bafMjVSBQ6e7vlO7NdkhXA/BJWL0go_Ge
6. https://pin.it/5YuoZXeZr </aside>

<aside> <img src="/icons/download_yellow.svg" alt="/icons/download_yellow.svg" width="40px" />

🍄Deliverables 6

Inhomogeneous Helmholtz Wave Propagation and Refractive Scattering Model

https://payhip.com/b/BacMg

Documents

• Computational Models
• Snippets
• A guide bridging the gap between abstract mathematical wave equations, Python simulation code, and intuitive physical concepts.

Exploration Frontiers

• First Born Approximation $\rightarrow$ Higher-Order Born Series
• Single Dielectric Cylinder $\rightarrow$ Multi-Cylinder Clusters
• Scalar Paraxial Beam $\rightarrow$ Vortex Beams & OAM
• Scalar Helmholtz Wave Equation $\rightarrow$ Vectorial Maxwell Equations

%%{init: {'theme': 'dark', 'themeVariables': { 'primaryColor': '#1E1B4B', 'primaryTextColor': '#F8FAFC', 'primaryBorderColor': '#6366F1', 'lineColor': '#38BDF8', 'tertiaryColor': '#5B21B6'}}}%%
flowchart TD
    %% Current Exploration Nodes
    subgraph Current ["CURRENT EXPLORATION"]
        A["Inhomogeneous Helmholtz Equation"] --> B["Paraxial Gaussian Beam Setup"]
        B --> C["Time-Harmonic Phase Evolution"]
    end

    %% Transition Node
    C --> D["<b>SIMULATION EXPANSION CORE</b>"]

    %% Potential Orientation Nodes
    subgraph Potential ["POTENTIAL FUTURE ORIENTATIONS"]
        D --> E["<b>Higher-Order Born Approximations</b><br/><i>Iterative Multiple Scattering</i>"]
        D --> F["<b>Multi-Cylinder Interference</b><br/><i>Complex Refractive Index Clusters</i>"]
        D --> G["<b>Vortex Beams & OAM</b><br/><i>Laguerre-Gaussian Modes</i>"]
        D --> H["<b>Vectorial Maxwell Equations</b><br/><i>Full Polarization & Interfaces</i>"]
    end

    %% Class Definitions - Modern Deep Color Palette
    classDef currentStyle fill:#1E1B4B,stroke:#6366F1,stroke-width:2px,color:#F8FAFC;
    classDef coreStyle fill:#5B21B6,stroke:#C084FC,stroke-width:2.5px,color:#FFFFFF;
    classDef futureStyle fill:#065F46,stroke:#2DD4BF,stroke-width:2px,color:#F0FDF4;

    class A,B,C currentStyle;
    class D coreStyle;
    class E,F,G,H futureStyle;

    %% Subgraph Containers
    style Current fill:#0F172A,stroke:#334155,stroke-width:1.5px,color:#A5B4FC;
    style Potential fill:#022C22,stroke:#1E3A8A,stroke-width:1.5px,color:#6EE7B7;

<aside> 👏

https://via-dean.gitbook.io/all/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/inhomogeneous-helmholtz-wave-propagation-and-refractive-scattering-model

</aside>

</aside>